The NFL Players Association's grievance against the NFL and its suspension of four players in connection to the New Orleans Saints "bounty" scheme will be decided in about a week, according to a source with knowledge of the situation.

The two sides argued before arbitrator Stephen Burbank for about 90 minutes in Philadelphia on Wednesday.

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Cleveland Browns linebacker Scott Fujita was the only one in attendance out of the players suspended for their roles in the pay-to-injure program. He was suspended three games by NFL Commissioner Roger Goodell.

Jeffrey Kessler argued on behalf of the NFLPA, which contended that Goodell does not have the authority to suspend the players for the bounty program because it is a salary-cap issue and not an on-field conduct issue. Salary-cap issues are ruled on by Burbank while on-field conduct is the domain of Goodell.

The league, represented by Gregg Levy, said the bounty program, which financially rewarded players for injuring opponents, falls under on-field conduct.

Goodell has suspended Saints defenders Jonathan Vilma (one season) and Will Smith (four games), along with current Green Bay Packers defensive lineman Anthony Hargrove (eight games) and Fujita for their roles in the scheme, which was implemented from 2009 to 2011. Fujita and Hargrove were members of the Saints during that time span.

Vilma declared his approval of the hearing via his Twitter account later Wednesday:

Hearings went well today. Nflpa did a tremendous job representing us, should
hear a decision soon. ?#fightinjustice

The NFLPA argued in a separate grievance two weeks ago that Goodell can't
rule or hear appeals for alleged behavior that took place on the field. A
ruling on that could come down any day, according to a league spokesman.

Saints head coach Sean Payton was suspended for a year, general manager
Mickey Loomis eight games and assistant head coach Joe Vitt six games. Former
defensive coordinator Gregg Williams, the architect of the program, has been
suspended indefinitely.

Vilma also has sued Goodell for defamation. All four players also have filed
to appeal to Goodell.